Spatiotemporal chaos in terms of unstable recurrent patterns

. Spatiotemporally chaotic dynamics of a Kuramoto--Sivashinsky system is described by means of an infinite hierarchy of its unstable spatiotemporally periodic solutions. An intrinsic parametrization of the corresponding invariant set serves as an accurate guide to the highdimensional dynamics, and the periodic orbit theory yields several global averages characterizing the chaotic dynamics. PACS numbers: 0230J, 0320, 0340, 0545 Introduction In recent years unstable periodic orbits have been shown to be an effective tool in the description of deterministic dynamical systems of low intrinsic dimension [1], in diagnosing deterministic chaos in noisy biological systems [2], and many other applications. The theory has been successfully applied to low-dimensional ordinary differential equations (deterministic chaos) and linear partial differential equations (semiclassical quantization). It is an open question whether the theory has anything to say about nonlinear partial differential equat...